Dynamics of generalized tachyon field

TL;DR

This paper analyzes the dynamics of a generalized tachyon field in Friedmann-Robertson-Walker spacetime, deriving the autonomous system and examining critical points and stability for specific cases, to understand potential universe evolutions.

Contribution

It introduces a general framework for the dynamical analysis of generalized tachyon fields and explores stability and final states for specific parameter choices.

Findings

Identification of critical points and their stability for $eta=1$ and $eta=2$

Analysis of the stability of the tachyon field at critical points

Discussion of possible final states of the universe

Abstract

We investigate the dynamics of generalized tachyon field in FRW spacetime. We obtain the autonomous dynamical system for the general case. Because the general autonomous dynamical system cannot be solved analytically, we discuss two cases in detail: $\beta=1$ and $\beta=2$. We find the critical points and study their stability. At these critical points, we also consider the stability of the generalized tachyon field, which is as important as the stability of critical points. The possible final states of the universe are discussed.